{"id":"https://openalex.org/W3003302312","doi":"https://doi.org/10.1109/tsmc.2020.2987335","title":"Adaptive Backstepping Control for Fractional-Order Nonlinear Systems With External Disturbance and Uncertain Parameters Using Smooth Control","display_name":"Adaptive Backstepping Control for Fractional-Order Nonlinear Systems With External Disturbance and Uncertain Parameters Using Smooth Control","publication_year":2020,"publication_date":"2020-05-05","ids":{"openalex":"https://openalex.org/W3003302312","doi":"https://doi.org/10.1109/tsmc.2020.2987335","mag":"3003302312"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2020.2987335","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2020.2987335","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.00162","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011833760","display_name":"Xinyao Li","orcid":"https://orcid.org/0000-0001-8683-3019"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xinyao Li","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-8683-3019","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100344158","display_name":"Changyun Wen","orcid":"https://orcid.org/0000-0001-9530-360X"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Changyun Wen","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-9530-360X","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055373759","display_name":"Ying Zou","orcid":"https://orcid.org/0000-0002-1410-1449"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Ying Zou","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-1410-1449","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":6.997,"has_fulltext":false,"cited_by_count":86,"citation_normalized_percentile":{"value":0.97529797,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"51","issue":"12","first_page":"7860","last_page":"7869"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.9173111319541931},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.8708093166351318},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6585168242454529},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6527173519134521},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.6291422247886658},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6002585887908936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5850715041160583},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5653141736984253},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.49076518416404724},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4732188284397125},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43823081254959106},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4197801351547241},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3285195827484131},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2509540319442749},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24738216400146484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11082205176353455}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.9173111319541931},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8708093166351318},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6585168242454529},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6527173519134521},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.6291422247886658},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6002585887908936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5850715041160583},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5653141736984253},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.49076518416404724},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4732188284397125},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43823081254959106},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4197801351547241},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3285195827484131},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2509540319442749},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24738216400146484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11082205176353455},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsmc.2020.2987335","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2020.2987335","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.00162","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.00162","pdf_url":"https://arxiv.org/pdf/2002.00162","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/162385","is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/162385","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.00162","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.00162","pdf_url":"https://arxiv.org/pdf/2002.00162","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G241251031","display_name":null,"funder_award_id":"MOE2017-T2-1-050","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W148919764","https://openalex.org/W626737487","https://openalex.org/W1204148594","https://openalex.org/W1584611818","https://openalex.org/W1850511188","https://openalex.org/W1966553738","https://openalex.org/W1977447091","https://openalex.org/W2004202105","https://openalex.org/W2005174859","https://openalex.org/W2006236787","https://openalex.org/W2009279158","https://openalex.org/W2012736024","https://openalex.org/W2029057284","https://openalex.org/W2050580331","https://openalex.org/W2053757777","https://openalex.org/W2058860728","https://openalex.org/W2071298997","https://openalex.org/W2083559699","https://openalex.org/W2085560684","https://openalex.org/W2092861539","https://openalex.org/W2093275073","https://openalex.org/W2100546477","https://openalex.org/W2142142783","https://openalex.org/W2144956475","https://openalex.org/W2151015649","https://openalex.org/W2157347895","https://openalex.org/W2259227674","https://openalex.org/W2306943945","https://openalex.org/W2337611563","https://openalex.org/W2346126941","https://openalex.org/W2488956545","https://openalex.org/W2489553629","https://openalex.org/W2568770738","https://openalex.org/W2589174422","https://openalex.org/W2729691343","https://openalex.org/W2733667913","https://openalex.org/W2735398992","https://openalex.org/W2761636223","https://openalex.org/W2765719034","https://openalex.org/W2783107351","https://openalex.org/W2794318889","https://openalex.org/W2803051819","https://openalex.org/W2904005722","https://openalex.org/W2910278735","https://openalex.org/W2916270127","https://openalex.org/W2943312863","https://openalex.org/W2970203041","https://openalex.org/W4240465921","https://openalex.org/W6671984239","https://openalex.org/W6766632604"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W2186140227","https://openalex.org/W2534185822","https://openalex.org/W2132535444","https://openalex.org/W1847613412","https://openalex.org/W4382203996","https://openalex.org/W1934622834","https://openalex.org/W2015036175"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"consider":[4],"controlling":[5],"a":[6,66,101],"class":[7],"of":[8,46,50,81,88,96,117],"single-input\u2013single-output":[9],"(SISO)":[10],"commensurate":[11],"fractional-order":[12,97],"nonlinear":[13],"systems":[14],"with":[15,31],"parametric":[16],"uncertainty":[17],"and":[18,43,92],"external":[19],"disturbance.":[20,48],"Based":[21],"on":[22],"the":[23,39,44,56,79,85,115,118],"backstepping":[24],"approach,":[25],"an":[26,59],"adaptive":[27,32],"controller":[28],"is":[29,62,71],"proposed":[30,119],"laws":[33],"that":[34,70],"are":[35,105,124],"used":[36],"to":[37,64,74,100],"estimate":[38],"unknown":[40,47],"system":[41,98],"parameters":[42],"bound":[45],"Instead":[49],"using":[51,108],"discontinuous":[52],"functions,":[53],"such":[54],"as":[55],"sign":[57],"function,":[58],"auxiliary":[60],"function":[61],"employed":[63],"obtain":[65],"smooth":[67],"control":[68,120],"input":[69],"still":[72],"able":[73],"achieve":[75],"perfect":[76,94],"tracking":[77,95],"in":[78],"presence":[80],"bounded":[82],"disturbances.":[83],"Indeed,":[84],"global":[86],"boundedness":[87],"all":[89],"closed-loop":[90],"signals":[91],"asymptotic":[93],"output":[99],"given":[102],"reference":[103],"trajectory":[104],"proved":[106],"by":[107],"fractional":[109],"directed":[110],"Lyapunov":[111],"method.":[112],"To":[113],"verify":[114],"effectiveness":[116],"method,":[121],"simulation":[122],"examples":[123],"presented.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}